You can throw with a torn labrum in your throwing shoulder. It just tends to lead to pain and soreness, especially with repeating the throwing motion over and over. When you take hits on your shoulder with the labrum injury, it aggravates the pain, and can lead to impairment of your throwing motion due to the pain. In short, you'll typically throw with less velocity with a labrum injury, and as the pain increases, that velocity goes even lower.

With a non-throwing shoulder injury, he may have pain when he gets hit, but it won't affect the throwing motion or velocity/accuracy of his throws. As long as he has a reasonable pain tolerance threshold, he'll be fine. Lots and lots of professional athletes play for years with torn labrums. Many won't have them surgically repaired until they retire. This includes baseball players who have to regularly throw. The only ones who typically will have their labrums fixed right away are pitchers and catchers.